Pexeso

The drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares to make a pexeso. What dimension must squares have if their side is larger than 3cm and less than 10cm?

Correct answer:

x₁ =  60 mm
x₂ =  40 mm

Step-by-step explanation:

$$\begin{gathered} a=60\text{cm}\to \text{mm}=60\cdot 10\text{mm}=600\text{mm} \\ b=840\text{mm} \\ 600=2^3\cdot 3\cdot 5^2 \\ 840=2^3\cdot 3\cdot 5\cdot 7 \\ \text{GCD}(600,840)=2^3\cdot 3\cdot 5=120 \\ y=GCD(a,b)=GCD(600,840)=120 \\ 30<x<100 \\ {x}_1=y/2=120/2=60\text{mm} \end{gathered}$$

$x_2=y/3=120/3=40\text{mm}$

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